You can do the snip with very little emotional trauma. Wrap the chick loosely in a paper towel, leaving enough toweling over the top so you can cover her head. Have a lunch sized paper bag handy. Hold the chick in your left hand, position the garden clippers at the top of her neck with your right hand. Fold the paper towel over the top. You won't even need to watch. Simply place the clippers in position, fold paper towel over top, do a quick snip, and drop the entire thing into the paper bag. Fold top down, and give her a burial in the yard. You can dig the hole before hand.
If you are going to hatch chicks, it's imperative that you be able to euthanize those chicks that need it. If you can't do so, or don't have some one to do it for you, you should decide not to hatch chicks again. Culling goes with the territory of hatching.